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Consider a four-year bond with a 10 percent coupon paid semiannually (or 5 percent paid every...

Consider a four-year bond with a 10 percent coupon paid semiannually (or 5 percent paid every 6 months) and an 8 percent rate of return (rb). Suppose that the rate of return increases by 10 basis points (1/10 of 1 percent) from 8 to 8.10 percent. Then, using the semiannual compounding version of the duration model shown above, how much is the percentage change in the bond's price?

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Expert Solution

Statement showing price of bond:      (assume face value to be $1000, in case of semiannual years to maturity will be 8 years, coupon payment= 1000*0.05=$50, yield is 4%)
Particulars Time PVf @4% Amount PV
Cash Flows (Interest)           1.00 0.9615          50.00          48.08
Cash Flows (Interest)           2.00 0.9246          50.00          46.23
Cash Flows (Interest)           3.00 0.8890          50.00          44.45
Cash Flows (Interest)           4.00 0.8548          50.00          42.74
Cash Flows (Interest)           5.00 0.8219          50.00          41.10
Cash Flows (Interest)           6.00 0.7903          50.00          39.52
Cash Flows (Interest)           7.00 0.7599          50.00          38.00
Cash Flows (Interest)           8.00 0.7307          50.00          36.53
Cash flows (Maturity Amount)           8.00      0.7307    1,000.00       730.70
Current Bond Price    1,067.34
Price of bond= $1067.34
Statement showing price of bond:      (assume face value to be $1000, in case of semiannual years to maturity will be 8 years, coupon payment= 1000*0.05=$50, yield is 4.05%)
Particulars Time PVf @4.05% Amount PV
Cash Flows (Interest)           1.00 0.9611          50.00          48.05
Cash Flows (Interest)           2.00 0.9237          50.00          46.18
Cash Flows (Interest)           3.00 0.8877          50.00          44.39
Cash Flows (Interest)           4.00 0.8532          50.00          42.66
Cash Flows (Interest)           5.00 0.8200          50.00          41.00
Cash Flows (Interest)           6.00 0.7880          50.00          39.40
Cash Flows (Interest)           7.00 0.7574          50.00          37.87
Cash Flows (Interest)           8.00 0.7279          50.00          36.39
Cash flows (Maturity Amount)           8.00      0.7279    1,000.00       727.90
Current Bond Price    1,063.84
Price of bond= $1063.84
Percentage change in bond price=(1063.84-1067.34)/1067.34*100= -0.33%

jeff jeffy answered 2 years ago
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